1. Field of the Invention
This invention relates generally to improvements in digital signal processing and specifically to a system and method for enhancing the efficiency of downsampling operations.
2. Description of the Background Art
The increased use of digital audio and video in the consumer market has challenged designers to produce digital signal processing technology with superior performance while using economical components. Often digital techniques which are well-known in the art require expensive processing hardware. In order to make use of inexpensive hardware, new techniques must be invented.
One technique that is used in digital signal processing is downsampling. The need for downsampling arises when the source of digitized signals provides digital samples at a higher sampling rate than the receiver of the digital signals can accept. In the case where the source sampling rate MR is an integral multiple M of the receiving sampling rate R, it would appear that simply deleting (M-1) samples out of M samples would yield a digital signal of the correct sample receiving rate R. In reality, this significantly reduces the accuracy of the resultant signal.
In order to downsample, defined as converting a higher sampling rate digital signal to a lower sampling rate digital signal, a downsampling filter is required. This downsampling filter makes use of the signal content of a number of neighboring samples from the digital signal at the MR rate to give a best representation of the signal at the R rate. The downsampling filter is often implemented as a Finite Impulse Response (FIR) filter. Let the digital signal at the rate of MR be represented by the function x(n) of the discrete variable n, and the corresponding digital signal at the rate of R be represented by the function y(m) of the discrete variable m. In this case the discrete variable m occurs once for every M'th occurrence of discrete variable n. If x(n) is known, a FIR filter representation of the calculation of y(m) from x(n) may be expressed by the following equation: ##EQU1##
where k is the summation index, h(k) are constants called the filter coefficients, and N is called the length of the filter.
In the case of digital audio, it is often necessary to downsample from a digital audio bitstream arriving at a rate twice that which can be accepted by a low-cost digital-to-analog converter (DAC). However, in the case of digital audio, very high quality is required and this causes the number N of filter coefficients h(k) to be large. The result is that both the processing power required from a digital signal processing (DSP) microprocessor and the size of the memory required to store the set of N coefficients cannot be realized by the most economical devices.